Yes, you can use multiple availability zones while using a network load balancer in AWS. This, in fact, increases the fault tolerance of your application. One thing you've to keep in mind is that multiple availability zones can only be enabled before the load balancer is created. You cannot enable or disable after it's created.
When you enable an Availability Zone, you specify one subnet from that Availability Zone. Elastic Load Balancing creates a load balancer node in the Availability Zone and a network interface for the subnet (the description starts with "ELB net" and includes the name of the load balancer). Each load balancer node in the Availability Zone uses this network interface to get a static IP address. Note that you can view this network interface but you cannot modify it.